Stability of the Ricci flow at Ricci-flat metrics

Communications in Analysis and Geometry

Volumn 10, Issue 4, 2002, Pages 741-777

  Guenther, Christine ^a   Isenberg, James ^a   Knopf, Dan ^a  

^a NONE

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EID: 0041848363     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.2002.v10.n4.a4     Document Type: Article

References (39)

1. U. Abresch and J. Langer, The normalized curve shortening flow and homothetic solutions, J. Differential Geom., 23 (1986), 175-196.
2. H. Amann, Linear and quasilinear parabolic problems I: Abstract linear theory, Birkhäuser Verlag, Basel, (1995).
3. A. Avez, Le laplacien de Lichnerowicz sur les tenseurs, C.R. Acad. Sc.i Paris Sér A Math., 284 (1977), 1219-1220.
4. M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geom., 3 (1969), 379-392.
5. A. Besse, Einstein manifolds, Springer Verlag, Heidelberg, (1987).
6. J.-P. Bourguignon, Formules de Weitzenböck en dimension 4, Exposé XVI of 'Géométrie riemannienne en dimension 4: Séminaire Arthur Besse,' Cedic, Paris, (1981), 156-177.
7. J.-P. Bourguignon, Les surfaces K3, Exposé VIII of 'Géométrie riemannienne en dimension 4: Séminaire Arthur Besse,' Cedic, Paris, (1981), 308-333.
8. P. Butzer and H. Johnen, Lipschitz spaces on compact manifolds, J. Funct. Anal., 7 (1971), 242-266.
9. C. Buzzanca, The Laplacian of Lichnerowicz on tensors, Boll. Un. Mat. Ital. B (6), 3 (1984), 531-541.
10. H.-D. Cao, Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds, Invent. Math., 81 (1985), 359-372.
11. H.D. Cao and B. Chow, Recent developments on the Ricci flow, Bull. Amer. Math. Soc., 31(1) (1999), 59-74.
12. Ph. Clément, H.J.A.M. Heijmans, et al, One-parameter semigroups, (CWI Monograph, 5) North Holland, Amsterdam, 1987.
13. α and m, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 8 (1960), 217-222.
14. M. Carfora, J. Isenberg, and M. Jackson, Convergence of the Ricci flow for metrics with indefinite curvature, J. Differential Geom., 31 (1990), 249-263.
15. G. Da Prato and P. Grisvard, Equations d'évolution abstraites nonlinéaires de type parabolique, Ann. Mat. Pura. Appl., 120 (1979), 329-396.
16. G. Da Prato and A. Lunardi, Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space, Arch. Rational Mech. Anal., 101(2) (1988), 115-141.
17. D. DeTurck, Deforming metrics in the direction of their Ricci tensors, author's improved version of the article that originally appeared under the same title in J. Differential Geom., 18 (1983), 157-162.
18. G. Dore and A. Favini, On the equivalence of certain interpolation methods, Boll. Un. Mat. Ital. B (7), 4 (1987), 1227-1238.
19. D. Ebin, The manifold of Riemannian metrics, Proc. Sympos. Pure Math. (Global Analysis), 15 (1968), 11-40.
20. C.L. Epstein and M.I. Weinstein, A stable manifold theorem for the curve shortening equation, Comm. Pure Appl. Math., 40 (1987), 119-139.
21. R. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.), 7(1) (1982), 65-222.
22. R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom., 18 (1983), 255-306.
23. R. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom., 24 (1986), 153-179.
24. R. Hamilton, The Ricci flow on surfaces, in 'Mathematics and general relativity,' AMS Contemporary Mathematics, 71 (1988), 237-262.
25. R. Hamilton, The formation of singularities in the Ricci flow, Surveys in Differential Geometry, 2 (1995), International Press, 7-136.
26. R. Hamilton, Non-singular solutions of the Ricci flow on three-manifolds, Comm. Anal. Geom., 7(4) (1999), 695-729.
27. D. Henry, Geometric theory of semilinear parabolic equations, Springer Verlag, Berlin, (1981).
28. G. Huisken, Ricci deformation of the metric on a Riemannian manifold, J. Differential Geom., 21 (1985), 47-62.
29. A. Lichnerowicz, Propagateurs et commutateurs en relativité générale, Publ. Math. Inst. Hautes Études Scientifiques, 10 (1961).
30. J. Moser, On the volume element of a manifold, Trans. Amer. Math. Soc., 120 (1965), 286-294.
31. A. Beauville, J.P. Bourguignon, and M. Demazure eds., Géométrie des surfaces K3: modules et périodes, Séminaire Palaiseau, Société Mathématique de France, Paris, (1985).
32. G. Simonett, Center manifolds for quasilinear reaction-diffusion systems, Differential Integral Equations, 8(4) (1995), 753-796.
33. I.M. Singer and J.A. Thorpe, The curvature of 4-dimensional Einstein spaces, in 'Global Analysis: Papers in honor of K. Kodaira,' Princeton University Press, Princeton, (1969), 355-365.
34. Y.T. Siu, Every K3 surface is Kähler, Invent. Math., 73 (1983), 139-150.
35. A. Todorov, Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surfaces, Invent. Math., 61(3) (1980), 251-265.
36. A. Todorov, How many Kähler metrics has a K3 surface?, in 'Arithmetic and Geometry: Papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday,' 2, Birkhäuser, (1983), 451-463.
37. H. Triebel, Interpolation theory, function spaces, differential operators (rev. ed.), Johann Ambrosius Barth Verlag, Heidelberg, (1995).
38. S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampere equation I, Comm. Pure Appl. Math., 31 (1978), 339-411.
39. R. Ye, Ricci flow, Einstein metrics, and space forms, Trans. Amer. Math. Soc., 338(2) (1993), 871-896.